Wei Liu is a professor of statistics at the University of Southampton, UK. Dr. Liu has published more than 80 papers in peer-reviewed journals, including Annals of Statistics, Journal of the American Statistical Association, Journal of the Royal Statistical Society, Biometrika, and Biometrics. His research encompasses multiple comparison, simultaneous inference, and sequential methods.
Simultaneous confidence bands enable more intuitive and detailed inference of regression analysis than the standard inferential methods of parameter estimation and hypothesis testing. Simultaneous Inference in Regression provides a thorough overview of the construction methods and applications of simultaneous confidence bands for various inferential purposes. It supplies examples and MATLAB® programs that make it easy to apply the methods to your own data analysis. The MATLAB programs, along with color figures, are available for download on www.personal.soton.ac.uk/wl/mybook.html
Most of the book focuses on normal-error linear regression models. The author presents simultaneous confidence bands for a simple regression line, a multiple linear regression model, and polynomial regression models. He also uses simultaneous confidence bands to assess part of a multiple linear regression model with the zero function, to compare two regression models, and to evaluate more than two regression models. The final chapter demonstrates the use of simultaneous confidence bands in generalized linear regression models, such as logistic regression models.
This book shows how to employ simultaneous confidence bands to make useful inferences in regression analysis. The topics discussed can be extended to functions other than parametric regression functions, offering novel opportunities for research beyond linear regression models.
Introduction to Linear Regression Analysis. Confidence Bands for One Simple Regression Model. Confidence Bands for One Multiple Regression Model. Assessing Part of a Regression Model. Comparison of Two Regression Models. Comparison of More Than Two Regression Models. Confidence Bands for Polynomial Regression. Confidence Bands for Logistic Regression. Appendices. Bibliography. Index.
With examples and MATLAB® programs that make it easy to apply the methods to your own data analysis, this book provides a thorough overview of the construction methods and applications of simultaneous confidence bands for various inferential purposes. Most of the text covers normal-error linear regression models, although the author also describes the logistic regression model to show how simultaneous confidence bands can be constructed and used for generalized linear regression models. The MATLAB programs, along with color figures, are available for download on the author´s website.
I like in particular this book since almost all results are given with proofs and that these proofs are easy to understand having some knowledge in linear models. It is especially helpful that the geometric ideas behind the proofs are worked out and presented with many illustrations. Together with the comprehensive review of the published literature and the presentation of some unsolved problems, this book is very valuable for researchers. It is also very recommendable for practitioners since the ideas of the concepts are worked out clearly and many examples and figures are presented where the confidence bands are applied to real data. MATLAB programs for all methods can be downloaded from the author´s website.
—Christine Müller, Biometrical Journal 53 (2011)
This book provides a comprehensive discussion of methods for determining simultaneous confidence bands in regression. ... The book provides a valuable up-to-date review of work in this area.
—David J. Hand, International Statistical Review (2011), 79
... definitely fills a significant niche, providing practitioners with powerful inference tools for parametric regression and stimulating further research in this important area.
— Tatyana Krivobokova, Georg-August- Univer,citat Gottingen, Royal Statistics Society, February 2012
The use of simultaneous confidence bands in linear regression is a vibrant area of research. This book presents an overview of the methodology and applications, including necessary background material on linear models.
Über den Autor
Wei Liu is a professor of statistics at the University of Southampton, UK. Dr. Liu has published more than 80 papers in peer-reviewed journals, including Annals of Statistics, Journal of the American Statistical Association, Journal of the Royal Statistical Society, Biometrika, and Biometrics. His research encompasses multiple comparison, simultaneous inference, and sequential methods.
Inhaltsverzeichnis
Introduction to Linear Regression Analysis Linear regression models Parameter estimation Testing hypotheses Confidence and prediction intervals Confidence Bands for One Simple Regression Model Preliminaries Hyperbolic bands Three-segment bands Two-segment bands Other confidence bands Extensions and restrictions of a confidence band Comparison of confidence bands Confidence bands for percentiles and tolerance bands Bayesian simultaneous credible bands Confidence Bands for One Multiple Regression Model Hyperbolic bands over the whole space Hyperbolic bands over a rectangular region Constant width bands over a rectangular region Hyperbolic bands over an ellipsoidal region Constant-width bands over an ellipsoidal region Other confidence bands Assessing Part of a Regression Model Partial F test approach Hyperbolic confidence bands Assessing equivalence to the zero function Comparison of Two Regression Models Partial F test approach Hyperbolic bands over the whole space Confidence bands over a rectangular region Confidence bands over an ellipsoidal region Assessing the equivalence of two models Comparison of More Than Two Regression Models Partial F test approach Hyperbolic confidence bands for all contrasts Bands for finite contrasts over rectangular region Bands for finite contrasts over ellipsoidal region Equivalence of more than two models Confidence Bands for Polynomial Regression Confidence bands for one model Confidence bands for part of a polynomial model Comparison of two polynomial models Comparison of more than two polynomial models Confidence Bands for Logistic Regression Introduction to logistic regression Bands for one model Bands for comparing two models Bands for comparing more than two models Appendix A: Approximation of the Percentile of a Random Variable Appendix B: Computation of Projection pi (t,P,Xr) Appendix C: Computation of Projection pi*(t,W,X2) Appendix D: Principle of Intersection-Union Test Appendix E: Computation of the K-Functions in Chapter 7 Bibliography Index
Klappentext
The use of simultaneous confidence bands in linear regression is a vibrant area of research. This book presents an overview of the methodology and applications, including necessary background material on linear models.
